SALT LAKE CITY — Maybe it’s the quirky name of the school, ‘‘Gonzaga.’’ Or its pint-sized enrollment of 4,900. Or the fact that employees at one office in its hometown are so gaga over the ’Zags, they wore their hair long at work this week as a shout-out to the team’s best player, flowing-tressed 7-footer Kelly Olynyk.

Whatever the reason for all the fun-spirited underdog love Gonzaga typically engenders this time of year, it’s time to get over it.

Coach Mark Few’s team left behind its little-team-that-could credentials long ago. As if to accentuate that point, this year, the ’Zags (31-2) come into the NCAA Tournament with a big, fat ‘1’ by their name — top-seeded in the West, top-ranked in the Associated Press poll, and top-heavy with expectations.

They open the tournament Thursday against 16th-seeded Southern (23-9), champion of the Southwestern Athletic Conference.

‘‘We’re just going to approach it like we did all those other games,’’ Few said. ‘‘This entire year, we’re 33 games in, and every game we’ve been the highest-rated team. If it ain’t broke, don’t fix it, is my motto.’’

Of course, it’s accurate to say the success story produced by a school like Gonzaga — a private, liberal arts, Jesuit institution in Spokane, Wash. — is still something of an anomaly in a college landscape filled with behemoth universities, their multimillion-dollar budgets, and the mega-conferences they play in.

But the Bulldogs, champions of the West Coast Conference, stack up against the best and have now for more than a decade.

Their 15-year string of trips to the NCAA Tournament is surpassed only at Duke, Kansas, and Michigan State — a stretch so long that hardly anyone close to the program remembers anything else.

So numbingly successful have the Zags been over the years that a different line of thinking has evolved — a theory that resonates louder the closer you get to their home campus.

Maybe Gonzaga hasn’t accomplished enough.

Since putting itself on the map in earnest with three straight Sweet 16 appearances from 1999-2001, Gonzaga has made it to the second weekend only twice. Four times since 2002, the Bulldogs have lost to a worse-seeded team.

In other words, the same unpredictability that helped make the tournament — and Gonzaga — what they are has also undercut this school on a handful of occasions. This year’s group — Olynyk, Kevin Pangos, Elias Harris, David Stockton, and the rest — has a chance to do what Bulldog greats Adam Morrison, Casey Calvary, Ronny Turiaf, and Stockton’s father, Hall of Famer John Stockton, could not: take Gonzaga to the Final Four.

Earlier this week, Few said he’d sleep great if all these matchups were best-of-five affairs. But they’re not. And so, it’s tiny Southern — enrollment 6,900 out of Baton Rouge, La. — trying to become the first No. 16 to upset a No. 1, while Gonzaga tries to remember what it felt like to be that sort of underdog.

‘‘We’ve had some difficult matchups in the first round when we’ve been a 7 to a 10, they’ve sent us across the country in someone’s backyard,’’ Few said. ‘‘I think we approached it with a chip on our shoulder and went out there and were the aggressive team. We’ve been talking a lot about doing the same thing with this group.’’

Led in scoring by senior Derick Beltran (15.9 points per game), the Jaguars saw the symmetry in it all when their name came up opposite Gonzaga’s on Selection Sunday.

‘‘I’ve been using these guys all year long as an example to building a program,’’ coach Roman Banks said of Gonzaga. ‘‘I think they’re a true example of what we’re trying to do at Southern University.’’

Beltran said Banks reminds his players of a time, 20-30 years ago, when coach Ben Jobe had Southern etched as a perennial fixture in the March Madness bracket and nobody had ever heard of Gonzaga.

‘‘Tables are turned now,’’ Beltran said.

Southern’s ability to make history will depend on its ability to contain Olynyk, the junior from British Columbia, who averages 17.5 points and 7.2 rebounds and is widely regarded as one of the top five players in the country.

He has never considered himself a basketball historian — and doesn’t remember a time when Gonzaga was anything other than what it is today: a top-notch program with a virtually locked-in date in the tournament.

‘‘I didn’t know Gonzaga from Duke, really, when I was growing up,’’ Olynyk said. ‘‘But they had a decade of excellence and when they were recruiting us, we all became versed in it.’’